Analytical approach to investigate the effects of through-thickness stress on springback in bending of isotropic sheet metal

In contemporary sheet metal forming processes such as electromagnetic forming, the sheet is subjected to significant out-of-plane compression stress. This study focuses on predicting springback in isotropic sheet metal bending under through-thickness compressive normal stress. An analytical approach was employed to calculate the longitudinal stress distribution across the sheet thickness by utilizing equilibrium equations and applying the flow rule in incremental plasticity based on a power law hardening model. The reverse bending moment was then obtained from these calculations. During unloading, the springback was estimated by assuming linear elastic behavior and neglecting the Bauschinger effect through a superposition method. A case study was conducted on an aluminum alloy sheet with varying compressive stresses and bend curvatures. The comparison of springback angles with finite element modeling revealed that increasing compressive normal stress to 75% and 100% of yield stress resulted in a reduction in springback by 17.4% and 32%, respectively. At 75% yield stress, the numerical model exhibited only a 4.4% difference from the analytical model. Validation of the analytical model included a four-point bending test with varying initial bend curvatures and angles, demonstrating substantial agreement between experimental, numerical, and analytical outcomes.